Thread: Need help for one question

1. Need help for one question

(a) Find all nonsymmetric 2x2 matrices A such that AA^T =(A^T)A
(b) Let S(subscript1) be the set of all matrices found in part (a) and let S(subscript2) be the set of all 2x2 scalar matrices. Define W = S(subscript1) U S(subscript2)
(i) Show that W is a subspace of M(subscript2x2)
(ii) Find dim (W)

I'm really struggling in this class so i have no clue how to do this. Help?

2. Okay for part a i got that all matrices that are skew-symmetric will satisfy that property but now im having trouble finding part b.

3. Originally Posted by mapleleaf
(a) Find all nonsymmetric 2x2 matrices A such that AA^T =(A^T)A
(b) Let S(subscript1) be the set of all matrices found in part (a) and let S(subscript2) be the set of all 2x2 scalar matrices. Define W = S(subscript1) U S(subscript2)
(i) Show that W is a subspace of M(subscript2x2)
(ii) Find dim (W)

I'm really struggling in this class so i have no clue how to do this. Help?

a) Find the conditions so that $\displaystyle \left(\begin{array}{cc}a&b\\c&d\end{array}\right)\ left(\begin{array}{cc}a&c\\b&d\end{array}\right)=\ left(\begin{array}{cc}a&c\\b&d\end{array}\right)\l eft(\begin{array}{cc}a&b\\c&d\end{array}\right)\,\ ,\,AND\,\,\,b\neq c$

After this almost all will be clearer, but if there're more questions write back after solving the above.

Tonio

4. Originally Posted by mapleleaf
Okay for part a i got that all matrices that are skew-symmetric will satisfy that property but now im having trouble finding part b.

Nop, this isn't correct since skew matrices have only zeroes in their diagonals and this is not the case here

Tonio